How to set up accuracy of edge length overlay?
While it is not possible to increase the precision of the "Edge Length" overlay (as far as i know and after searching), there is a way to have a precise value displayed, BUT it's not "as easy" available and intuitive as activating the edge length.

What you may want to try is the "MeasureIT"-addon which comes with Blender.


It allows you to create a dynamic measurements.
I use Segment most the time to show the distance between 2 vertices (picture below).


As shown, the precision is set to 4 decimals after the point.

Expanding the shown measurement shows this:


Here you can deactivate it, change the color, size of the text, distance from object and many more things. Best to test and play around with to get the feel.

I hope it helps for your situation.